Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Table of contents

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[171.] LEMMA XI. PROP. LXXIX.
Page: 148 (124)
[172.] LEMMA XII. PROP. LXXX.
Page: 149 (125)
[173.] THEOR. XXXVIII. PROP. LXXXI.
Page: 149 (125)
[174.] PROBL. XXXII. PROP. LXXXII.
Page: 150 (126)
[175.] COROLL.
Page: 152 (128)
[176.] THEOR. XXXIX. PROP. LXXXIII.
Page: 153 (129)
[177.] ALITER affirmatiuè.
Page: 153 (129)
[178.] PROBL. XXXIII. PROP. LXXXIV.
Page: 154 (130)
[179.] SCHOLIVM.
Page: 155 (131)
[180.] THEOR. XL. PROP. LXXXV.
Page: 155 (131)
[181.] THEOR. XLI. PROP. LXXXVI.
Page: 156 (132)
[182.] COROLL. I.
Page: 157 (133)
[183.] COROLL. II.
Page: 157 (133)
[184.] THEOR. XLII. PROP. LXXXVII.
Page: 157 (133)
[185.] THEOR. XLIII. PROP. LXXXVIII.
Page: 158 (134)
[186.] LEMMA XIII. PROP. XIC.
Page: 160 (136)
[187.] THEOR. XLIV. PROP. XC.
Page: 161 (137)
[188.] COROLL. I.
Page: 162 (138)
[189.] COROLL. II.
Page: 163 (139)
[190.] COROLL. III.
Page: 163 (139)
[191.] THEOR. XLV. PROP. XCI.
Page: 163 (139)
[192.] COROLL. I.
Page: 164 (140)
[193.] COROLL. II.
Page: 164 (140)
[194.] THEOR. XLVI. PROP. XCII.
Page: 165 (141)
[195.] THEOR. XLVIII. PROP. XCIII.
Page: 166 (142)
[196.] PROBL. XXXIV. PROP. XCIV.
Page: 168 (144)
[197.] PROBL. XXXV. PROP. XCV.
Page: 169 (145)
[198.] PROBL. XXXVI. PROP. XCVI.
Page: 169 (145)
[199.] THEOR. XLVIII. PROP. XCVII.
Page: 170 (146)
[200.] COROLL.
Page: 171 (147)
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            <s xml:id="echoid-s5094" xml:space="preserve">In ſingulis enim figuris iuncta recta C D: </s>
            <s xml:id="echoid-s5095" xml:space="preserve">erit in tribus primis circa maio-
              <lb/>
            rem axim, recta C D maior C A (cum circulus ex C A ſit ſectioni
              <note symbol="a" position="left" xlink:label="note-0178-01" xlink:href="note-0178-01a" xml:space="preserve">92. h</note>
            ptus, ac propterea ſecet C D) ſed C A maior eſt G D, v thìc ad numeros
              <lb/>
            2, 3, & </s>
            <s xml:id="echoid-s5096" xml:space="preserve">5. </s>
            <s xml:id="echoid-s5097" xml:space="preserve">oſtenſum eſt, ergo C D eò ampliùs maior erit ipſa G D, ſiue
              <lb/>
            quadratum C D maius quadrato G D, vel duo ſimul C I, I D maiora
              <lb/>
            duobus ſimul G I, I D, quare dempto communi D I, erit quadratum C I
              <lb/>
            maius quadrato G I, vnde punctum C cadet infra G: </s>
            <s xml:id="echoid-s5098" xml:space="preserve">ſed A C, D G ſi-
              <lb/>
            mul conueniunt ad partes axis B R, vt ad num. </s>
            <s xml:id="echoid-s5099" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5100" xml:space="preserve">oſtendimus, ergo ipſa-
              <lb/>
            rum occurſus erit vltra axim B R.</s>
            <s xml:id="echoid-s5101" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5102" xml:space="preserve">In quarta demum figura, eſt C D minor C A (cum circulus ex C A ſit
              <lb/>
            Ellipſi circumſcriptus ) & </s>
            <s xml:id="echoid-s5103" xml:space="preserve">C A minor G D, prout ad num. </s>
            <s xml:id="echoid-s5104" xml:space="preserve">6. </s>
            <s xml:id="echoid-s5105" xml:space="preserve">huius
              <note symbol="b" position="left" xlink:label="note-0178-02" xlink:href="note-0178-02a" xml:space="preserve">ibidem.</note>
            monſtrauimus, quare C D erit omnino minor G D, ſiue quadratum C D
              <lb/>
            minus quadrato G D, vel duo ſimul C I, I D minora duobus ſimul G I,
              <lb/>
            I D; </s>
            <s xml:id="echoid-s5106" xml:space="preserve">quamobré dempto I D, erit C I minus G I, ſiue punctum C occurſus
              <lb/>
            inferioris perpendicularis A C cadet ſupra G occurſum ſuperioris D G;
              <lb/>
            </s>
            <s xml:id="echoid-s5107" xml:space="preserve">ſed tales perpendiculares A C, D G ſe mutuò ſecant (vt ſuperiùs oſten-
              <lb/>
            dimus ad num. </s>
            <s xml:id="echoid-s5108" xml:space="preserve">1.) </s>
            <s xml:id="echoid-s5109" xml:space="preserve">ad partes axis B R, quare ipſarum occurſus erit inter
              <lb/>
            contactus, & </s>
            <s xml:id="echoid-s5110" xml:space="preserve">minorem axim, ſed reſpectu maiorem axim M L ſe mutuò
              <lb/>
            ſecant vltra M L, vti paulò ante demonſtrauimus. </s>
            <s xml:id="echoid-s5111" xml:space="preserve">Quare in Ellipſi oc-
              <lb/>
            curſus huiuſmodi perpendicularium A C, D G cadet in angulo quadran-
              <lb/>
            tis M L G, qui deinceps eſt quadranti M L B, ad cuius peripheriam M A
              <lb/>
            B ductæ ſunt perpendiculares A C, D G, &</s>
            <s xml:id="echoid-s5112" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5113" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div520" type="section" level="1" n="214">
          <head xml:id="echoid-head219" xml:space="preserve">Pag. 147. ad finem Prop. 97.</head>
          <p>
            <s xml:id="echoid-s5114" xml:space="preserve">quodque de _MAXIMIS_ ſimilibus Ellipſibus angulo rectilineo inſcriptis
              <lb/>
            facillimùm eſt demonſtrare.</s>
            <s xml:id="echoid-s5115" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div521" type="section" level="1" n="215">
          <head xml:id="echoid-head220" xml:space="preserve">FINIS.</head>
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